For both their theoretical and practical impact, time-delay systems have been an enduring theme in the study of differential equations, stochastic processes, game theory, and systems theory. The subject has broad applications to a number of areas, including mechanical, electrical and chemical engineering, mathematics, biology, and economics.

This book is a self-contained, coherent presentation of the background and progress of the stability of time-delay systems. Focusing on techniques, tools, and advances in numerical methods and optimization algorithms, the authors develop material, which up until now, has been scattered in technical journals and conference proceedings. Special emphasis is placed on systems with uncertainty and stability criteria which can be computationally implemented.

Features and Topics:

* Systematic and comprehensive coverage of robust stability for time-delay systems, including time-domain and frequency-domain approaches

* Stability criteria formulated using linear matrix inequalities (LMI), providing a powerful toolbox for practicing engineers

* Strong stability conditions developed to provide a solid basis for design of feedback control and filtering

* Balance of intuition and rigor, stressing concepts rather than technical details

* Emphasis on comparisons and connections among various approaches

* Mathematical prerequisites integrated within each chapter, with more elementary material covered in two appendices

Requiring only basic knowledge of linear systems and Lyapunov stability theory, Stability of Time-Delay Systems will be accessible to a broad audience of researchers, professional engineers, and graduate students. It may be used for self-study or as a reference; portions of the text may be used in advanced graduate courses and seminars.

This book is a self-contained presentation of the background and progress of the study of time-delay systems, a subject with broad applications to a number of areas.

In the mathematical description of a physical or biological process, it is a common practice \0 assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho dology for analysis and control design for such systems, the lime-delay elements arc often either neglected or poorly approximated, which frequently results in analysis and simulation of insufficient accuracy, which in turns leads to poor performance of the systems designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriora ted perfonnances for the corresponding closed-loop systems."